LIFE HISTORY OF LAKE HERRING OF LAKE HURON 343 



found to be operative among the herring (see p. 370) and in part the result of the 

 retarding effect on growth of sexual maturation. According to these conclusions, 

 Lee's "phenomenon" is largely a natural one and not an error due to a faulty tech- 

 nique or to fallacious assumptions. It should appear in the calculated length values 

 of the mature lake herring of the younger age groups (5 years and younger) of a 

 year class. 



Erroi-s in computations of length may arise from causes other than those dis- 

 cussed. Other possible sources of error are: (1) all the scales of an individual do not 

 begin their development at the same time, (2) after they appear they may have dif- 

 ferent rates of growth, (3) annuli may vary in the time of their completion, and (4) 

 the length of the head, included in all measurements of the length of the body, may 

 vary with the size and the age of the fish. 



Some of these sources of error may be avoided easily, while others are known to 

 have virtually no effect upon the length computations of the herring under considera- 

 tion. Thus, the errors produced by the variation in the time of the appearance of 

 scales in an individual and by the differences in the growth rates of these scales are 

 eliminated largely by employing for study scales selected from a circumscribed area 

 on the body. The errors caused by the variation in the time of the completion of 

 annuli can not, it seems to me, be appreciably large in the herring, as this variation is 

 presumably no greater than that in the time of the resumption of accelerated growth 

 in the spring, which nonnally would not be expected to exceed a week among individ- 

 uals living under identical conditions of growth. With respect to the age variations 

 in head length, it has been concluded already (Table 9) that virtually none occur in 

 the adult herring under consideration. 



To recapitulate, it now appears that of the various possible factors that could 

 affect the accuracy of the computations of length based on scales, only two seem to be 

 significant in the lake herring. The firet factor, the employment of the anterior 

 radius of a scale for computations of length, discussed on pages 322 to 327, does not 

 affect the scale theory but only its erroneous application. Whereas the theory 

 assumes that the diameter of a scale increases in a direct ratio to the increase in the 

 length of the body, the investigators employ, out of necessity or for convenience, the 

 radius. I found (p. 325) "that the length computations based on the diameter are 

 always higher than those based on the anterior radius of a scale, and that the dif- 

 ference between the computations of the two series increases consistently with each 

 earlier year of life for which calculations are made, so that the maximum average 

 difference of 13 miUimeters is found in year I." The second significant factor, the 

 disproportionate increase in length of body and scale, involves the theory itself. I 

 found (p. 323) that neither the diameter nor the anterior radius of a scale increased 

 in length strictly proportionally with that of the body. No general formula can 

 correct the errors caused by the disproportionate increase of body and scale length. 

 To eliminate the errors due to this factor corrections must be made for each age 

 group separately. It is probably for this reason tliat the general corrective factore 

 proposed by Doctor Jarvi (see p. 305) for his Coregonus alhula did not hold for his 

 fish of all ages. Corrections for the above two factors apparently bring the computed 

 lengths for the herring of the third and fourth years of life more nearly into agreement 

 99760—29 6 



